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Thus they are not adequately sampled in conventional simulation approaches. Activated dynamics methods provide one alternative that overcomes this sampling problem, although stochastic dynamics has also been applied to barrier crossing phenomena (see Chapt. 3). Special simulation techniques have been developed which make possible the efficient determination of trajectories of relevance in calculating the rates for activated p r o c e s ~ e s . These ~ ~ ~ -techniques, ~~~ which were earlier applied to small-moleculecollision dynamics125-127and to vacancy diffusion dynamics in regular solids,128 represent a synthesis of molecular dynamics methods and transition-state theory that can be used with the more general dynamics techniques discussed above.

RN)refer to the N atoms in the reaction zone. 44 DYNAMICAL SIMULATION METHODS These modified equations of motion are solved numerically using a Verlet type of algorithm which includes the effect due to the presence of Langevin forceswJo2(see Chapt. G). There are some limitations to the stochastic boundary molecular dynamics approach in its present form. Since the method is limited to a local region, it neglects explicit effects of the rest of the system. Extensions of the theory to include the influence of low-frequency motions and fluctuating long-range electrostatic interactions on the local dynamics are possible.